python open file browser to Group directory of blend file?
Via the link or append operator

Test script, template file as a scene property in way of example, possibly better set as an addon preference. 

import bpy
from bpy.props import StringProperty

class HelloWorldPanel(bpy.types.Panel):
    """Creates a Panel in the Object properties window"""
    bl_label = "Hello World Panel"
    bl_idname = "OBJECT_PT_hello"
    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "scene"

    def draw(self, context):
        layout = self.layout
        scene = context.scene
        col = layout.column()
        col.prop(scene, "template_file")
        # check if fp exists
        col.operator_context = 'INVOKE_DEFAULT'
        if True: 
            # write an op to 
            directory = "%s/Group/" % (scene.template_file)
            op = col.operator("wm.append")
            op.directory = directory
            op.instance_groups = True


def register():
    bpy.types.Scene.template_file = StringProperty(
            subtype='FILE_PATH')

    bpy.utils.register_class(HelloWorldPanel)


def unregister():
    bpy.utils.unregister_class(HelloWorldPanel)
    # del prop


if __name__ == "__main__":
    register()


Alternatively A file test.blend that has 5 groups in it.

&gt;&gt;&gt; fp = "/home/batfinger/Desktop/test.blend"
&gt;&gt;&gt; with bpy.data.libraries.load(fp) as (data_in, data_out):
...     pass
...     

&gt;&gt;&gt; data_in.groups
['Group.004', 'Group.003', 'Group.002', 'Group.001', 'Group']


a group name above can be passed as filename argument to operator as show in 
Appending an Object Without A Link

Links re linking appending from files.

How to Link/Append a data-block using the Python API?

Import group from external blend file

How to search through multiple Blender files to find a specific object?